Equation of motion for a particle: Newton’s 2^nd law

Newton’s 2^nd law: The resultant of all the forces acting on a particle is proportional to the acceleration of the particle.

Newton’s 3^rd law: Each action has a reaction equal in magnitude, but opposite in direction

Equations of motion in a rectangular coordinate system: In a rectangular coordinate system the equations of motion can be represented by three scalar equations:

Example 1:

Example 2:

Equations of motion in normal and tangential (natural) coordinate systems: In a natural coordinate system the equations of motion can be represented by three scalar equations:

Example 3:

Equations of motion in Cylindrical coordinate systems: In a cylindrical coordinate system the equations of motion can be represented by three scalar equations:

Example 4:

Free-Body diagram: A diagram showing the particle under consideration and all the forces acting on the particle. Each force in this diagram must be labeled.

Gravity: The force of gravity is equal to the mass times the acceleration of gravity and is applied at the center of gravity (CG) of the body.

String or cable: A mechanical device that can only transmit a tensile force along itself.

Linear spring: A mechanical device which exerts a force proportional to its extension along its line of action.

Example 5:

Frictionless and massless pulleys: For a frictionless and massless pulley, the tension in the cable is the same on both sides of the pulley.

Example 6:

ã Mehrdad Negahban and the University of Nebraska, 1996-2002.

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Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526